8th grade solving equations with one expansion worksheets
These eight equations have variable terms on both sides and one solution each. Each has one set of parentheses, with four expansions on each side of the equals sign across the sheet. Easier uses integer values and integer solutions. On level introduces fractional factors and two half-integer solutions. Harder combines more negative and improper fractional factors with five noninteger solutions. The default key shows distribution, the solving steps and a check in both sides of the original grouped equation.
Free printable PDF worksheet, aligned to Common Core 8.EE.C.7.b.
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The kind of problems you'll get
Solve for the unknown variable. Show your steps and check your answer in the original equation.
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2 × m − 2 = 2 × (2 × m + 2)
Answer: m = −3
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2 × (2 × x + 1) = x + 5
Answer: x = 1
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−2 × (2 × z + 3) = −z − 6
Answer: z = 0
Every print pulls a fresh set of problems at this level, so a make-up test or a second sibling never gets the same sheet.
What's on an 8th grade sheet
- Solving equations with one expansion. Solve for the unknown variable. Show your steps and check your answer in the original equation. 8 problems per page.
Every version prints on US Letter or A4, with its answer key after the problems.
How to teach this
Have your child multiply every term inside the parentheses before collecting variable terms. Keep the sign on a negative factor through both products. Substitute into the original parentheses to check the answer.
Watch for: Apply the same operation to both sides of the equation. Keep the sign when subtracting a variable term or dividing by a negative coefficient.
Common questions about 8th grade solving equations with one expansion
- What does the answer key show?
- By default, each solution includes distribution, the equation steps, reasons and an original-equation check. Choose Answers only for final answers without the worked steps.
- What numbers are used?
- Easier has eight integer solutions. On level has six integer and two half-integer solutions. Harder has three integer and five noninteger solutions. Each setting includes exactly one zero solution.
- Can an equation have no solution?
- Every equation on this sheet has exactly one solution. Classifying other solution sets is a separate lesson.
Related worksheets
- 8th grade classifying linear solution sets Same grade, nearby skill
- 8th grade clearing fractional coefficients Same grade, nearby skill
- 8th grade equations in mixed numeric representations Same grade, nearby skill
- 8th grade equations requiring collection of like terms Same grade, nearby skill
- Solving equations with one expansion, all grades The full progression
- All 8th grade math worksheets Every skill at this level
- All 8th grade worksheets Everything at this level
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Aligned to Common Core 8.EE.C.7.b. Reviewed by the One more sheet team. Content version 241, updated October 2026.
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